Question 1068287
Draw a line that is the perpendicular bisector of AB and find the point O that is the intersection of the bisector and the circle. Label that point O.

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*[illustration gd12.JPG].
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OACB forms a cyclic quadrilateral and the opposite angles are supplementary.
So,
{{{ACB+AOB=180}}}
However AOB is fixed and independent of the choice of C.
That means that ACB is also fixed.
You also know that,
{{{CAB+CBA+ACB=180}}}
{{{CAB+CBA=180-ACB}}}
Since the right hand side is a fixed value, the sum of the other two angle is also fixed.